Achievement is a word that, in gamification especially, has several potential meanings and can cause significant confusion. In gamification, it is often associated with things like points and badges. The same can be said for video games these days (think Xbox achievements and Playstation trophies).
To confuse things more, people can be categorised in gamification and video games (using my user types or Bartle’s player types) as achievers. This makes it look a little like only one type of user will actually experience achievement.